The generator matrix

 1  1  1  1  1  X  1  0  X  X  1  1  1
 0  X  0 X+2  0  X X+2  X X+2 X+2  2 X+2  0
 0  0  2  0  0  0  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  2  2  0  2  0
 0  0  0  0  2  0  0  2  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  2  2  0  0  2  0

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+26x^8+93x^10+128x^11+264x^12+264x^14+128x^15+93x^16+26x^18+1x^26

The gray image is a code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00485 seconds.